Q 9.129. Simplify:聽162x10y22x6y6.... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 9.129. (page 1083)

Simplify: $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$ .

Short Answer

Expert verified

Simplified form of $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$ is $\frac{9 x^{2}}{y^{2}}$

Step by step solution

Step 1. Given information.

Given a fraction $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$ .

Step 2. Rewrite using the quotient property of square roots.

Quotient property of square roots says that if a, b are non-negative number and $b 鈮� 0$ , then $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ .

It follows that $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}} = \sqrt{\frac{162 x^{10} y^{2}}{2 x^{6} y^{6}}}$ .

Step 3. Remove common factors.

Remove common factor as follows.

$\begin{array}{rcl} \sqrt{\frac{162 x^{10} y^{2}}{2 x^{6} y^{6}}} & = & \sqrt{\frac{2 路 81 路 x^{6} 路 x^{4} 路 y^{2}}{2 路 x^{6} 路 y^{2} 路 y^{4}}} \\ = & \sqrt{\frac{81 x^{4}}{y^{4}}} \end{array}$

Step 4. Simplify the radical.

Simplify the radical as follows.

$\begin{array}{rcl} \sqrt{\frac{81 x^{4}}{y^{4}}} & = & \sqrt{\frac{{(9 x^{2})}^{2}}{{(y^{2})}^{2}}} \\ = & \frac{9 x^{2}}{y^{2}} \end{array}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify: $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite using the quotient property of square roots.

Step 3. Remove common factors.

Step 4. Simplify the radical.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Discrete Mathematics

Probability and Statistics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

91影视

Simplify:162x10y22x6y6.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite using the quotient property of square roots.

Step 3. Remove common factors.

Step 4. Simplify the radical.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Discrete Mathematics

Probability and Statistics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

Simplify: $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$ .